Journal of Function Spaces http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Jordan Type Inequalities for Hyperbolic Functions and Their Applications Sun, 01 Mar 2015 14:16:04 +0000 http://www.hindawi.com/journals/jfs/2015/370979/ We present the best possible parameters p, such that the double inequality holds for all . As applications, some new inequalities for certain special function and bivariate means are found. Zhen-Hang Yang and Yu-Ming Chu Copyright © 2015 Zhen-Hang Yang and Yu-Ming Chu. All rights reserved. Existence and Asymptotic Behaviour of Solutions of Differential and Integral Equations in Some Function Spaces Sun, 01 Mar 2015 10:25:40 +0000 http://www.hindawi.com/journals/jfs/2015/235043/ Józef Banaś, Mohamed Abdalla Darwish, Leszek Olszowy, and Kishin Sadarangani Copyright © 2015 Józef Banaś et al. All rights reserved. Some Basic Properties of Certain New Subclass of Meromorphic Functions Sun, 01 Mar 2015 08:03:31 +0000 http://www.hindawi.com/journals/jfs/2015/196060/ We introduce and investigate a new subclass of meromorphic functions. Some interesting properties such as inclusion relationship, coefficient estimates, neighborhoods, and partial sums are proved. Connections of the results with known results are also considered. Lei Shi and Zhi-Gang Wang Copyright © 2015 Lei Shi and Zhi-Gang Wang. All rights reserved. Fixed Points of Modified -Contractive Mappings in Complete Metric-Like Spaces Sat, 28 Feb 2015 09:48:32 +0000 http://www.hindawi.com/journals/jfs/2015/270971/ We introduce the notion of modified -contractive mappings in the setting of complete metric-like spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature. Hamed H. Alsulami, Erdal Karapınar, and Hossein Piri Copyright © 2015 Hamed H. Alsulami et al. All rights reserved. Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric Points Wed, 25 Feb 2015 08:33:12 +0000 http://www.hindawi.com/journals/jfs/2015/145242/ We introduce two subclasses of biunivalent functions and find estimates on the coefficients and for functions in these new subclasses. Also, consequences of the results are pointed out. Şahsene Altınkaya and Sibel Yalçın Copyright © 2015 Şahsene Altınkaya and Sibel Yalçın. All rights reserved. Picard Sequence and Fixed Point Results on -Metric Spaces Wed, 25 Feb 2015 07:06:24 +0000 http://www.hindawi.com/journals/jfs/2015/189861/ We obtain some fixed point results for single-valued and multivalued mappings in the setting of a -metric space. These results are generalizations of the analogous ones recently proved by Khojasteh, Abbas, and Costache. Marta Demma and Pasquale Vetro Copyright © 2015 Marta Demma and Pasquale Vetro. All rights reserved. A New Characterization of -Uniformly Rotund Banach Space Tue, 24 Feb 2015 14:19:03 +0000 http://www.hindawi.com/journals/jfs/2015/865305/ A new characterization of -uniformly rotund Banach space with is given. Moreover, a corresponding result in the locally -uniformly rotund Banach space with is given. Suyalatu Wulede, Tingting Li, and Xuan Qin Copyright © 2015 Suyalatu Wulede et al. All rights reserved. Continuous Dependence of the Solutions of Nonlinear Integral Quadratic Volterra Equation on the Parameter Mon, 23 Feb 2015 08:07:24 +0000 http://www.hindawi.com/journals/jfs/2015/471235/ We prove results on the existence and continuous dependence of solutions of a nonlinear quadratic integral Volterra equation on a parameter. This dependence is investigated in terms of Hausdorff distance. The considerations are placed in the Banach space and the Fréchet space. Szymon Dudek and Leszek Olszowy Copyright © 2015 Szymon Dudek and Leszek Olszowy. All rights reserved. Inequalities Characterizing Linear-Multiplicative Functionals Mon, 23 Feb 2015 07:47:02 +0000 http://www.hindawi.com/journals/jfs/2015/945758/ We prove, in an elementary way, that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities, then it is a linear and multiplicative functional. Moreover, we determine all Jensen concave and supermultiplicative operators , where and are compact Hausdorff spaces. Włodzimierz Fechner Copyright © 2015 Włodzimierz Fechner. All rights reserved. The Generalized Green’s Function for Boundary Value Problem of Second Order Difference Equation Mon, 23 Feb 2015 06:37:20 +0000 http://www.hindawi.com/journals/jfs/2015/201946/ Let and . In this paper, by building the generalized Green’s function for the problems, we study the solvability of the S-L problem , , , and the periodic S-L problem , , where the parameter is an eigenvalue of the linear problem , , or the problem , , and , is defined and real valued on , and in the periodic S-L problem we have . Xiaoling Han and Juanjuan Huang Copyright © 2015 Xiaoling Han and Juanjuan Huang. All rights reserved. Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology Sun, 22 Feb 2015 14:39:14 +0000 http://www.hindawi.com/journals/jfs/2015/796753/ Let be a completely regular Hausdorff space and let and be Banach spaces. Let be the space of all -valued bounded, continuous functions on , equipped with the strict topology . We study the relationship between important classes of -continuous linear operators (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. Marian Nowak Copyright © 2015 Marian Nowak. All rights reserved. Some Results for Periodic Solutions of a Kind of Liénard Equation Sun, 22 Feb 2015 06:58:53 +0000 http://www.hindawi.com/journals/jfs/2015/519747/ We investigate the following Liénard-type -Laplacian equation with a deviating argument . Some new criteria for guaranteeing the existence and uniqueness of periodic solutions of this equation are given by using the Manásevich-Mawhin continuation theorem and some analysis techniques. Our results hold under weaker conditions than some known results from the literature and are more effective. In the last section, an illustrative example is provided to demonstrate the applications of the theoretical results. Yong Wang and Xiangyi Yi Copyright © 2015 Yong Wang and Xiangyi Yi. All rights reserved. On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains Thu, 19 Feb 2015 10:34:05 +0000 http://www.hindawi.com/journals/jfs/2015/265245/ New sharp estimates of traces of Bergman type spaces of analytic functions in bounded strictly pseudoconvex domains are obtained. These are, as far as we know, the first results of this type which are valid for any bounded strictly pseudoconvex domains with smooth boundary. Romi F. Shamoyan and Olivera R. Mihić Copyright © 2015 Romi F. Shamoyan and Olivera R. Mihić. All rights reserved. A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations Tue, 17 Feb 2015 08:22:06 +0000 http://www.hindawi.com/journals/jfs/2015/643969/ We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations. This uniqueness theorem can replace the repeated proofs for uniqueness of the relevant solutions of given equations while we investigate the stability of functional equations. Yang-Hi Lee and Soon-Mo Jung Copyright © 2015 Yang-Hi Lee and Soon-Mo Jung. All rights reserved. Volterra Type Integral Operators and Composition Operators on Model Spaces Thu, 12 Feb 2015 13:08:30 +0000 http://www.hindawi.com/journals/jfs/2015/467802/ We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems can be used to study a number of other operator theoretic related problems in the spaces. Tesfa Mengestie Copyright © 2015 Tesfa Mengestie. All rights reserved. Ulam Problem for the Cosine Addition Formula in Sato Hyperfunctions Thu, 12 Feb 2015 09:49:38 +0000 http://www.hindawi.com/journals/jfs/2015/615167/ We prove the Ulam problem for the cosine addition formula in the spaces of Schwartz distributions and Sato hyperfunctions with respect to bounded distributions and bounded hyperfunctions. Jaeyoung Chung and Soon-Yeong Chung Copyright © 2015 Jaeyoung Chung and Soon-Yeong Chung. All rights reserved. Large Function Algebras with Certain Topological Properties Tue, 10 Feb 2015 12:55:42 +0000 http://www.hindawi.com/journals/jfs/2015/761924/ Let be a family of continuous functions defined on a compact interval. We give a sufficient condition so that contains a dense -generated free algebra; in other words, is densely -strongly algebrable. As an application we obtain dense -strong algebrability of families of nowhere Hölder functions, Bruckner-Garg functions, functions with a dense set of local maxima and local minima, and nowhere monotonous functions differentiable at all but finitely many points. We also study the problem of the existence of large closed algebras within where or . We prove that the set of perfectly everywhere surjective functions together with the zero function contains a -generated algebra closed in the topology of uniform convergence while it does not contain a nontrivial algebra closed in the pointwise convergence topology. We prove that an infinitely generated algebra which is closed in the pointwise convergence topology needs to contain two valued functions and infinitely valued functions. We give an example of such an algebra; namely, it was shown that there is a subalgebra of with generators which is closed in the pointwise topology and, for any function in this algebra, there is an open set such that is a Bernstein set. Artur Bartoszewicz and Szymon Głąb Copyright © 2015 Artur Bartoszewicz and Szymon Głąb. All rights reserved. Representation of Group Isomorphisms: The Compact Case Tue, 03 Feb 2015 08:54:51 +0000 http://www.hindawi.com/journals/jfs/2015/879414/ Let be a discrete group and let and be two subgroups of -valued continuous functions defined on two 0-dimensional compact spaces and . A group isomorphism defined between and is called separating when, for each pair of maps satisfying that , it holds that . We prove that under some mild conditions every biseparating isomorphism can be represented by means of a continuous function as a weighted composition operator. As a consequence we establish the equivalence of two subgroups of continuous functions if there is a biseparating isomorphism defined between them. Marita Ferrer, Margarita Gary, and Salvador Hernández Copyright © 2015 Marita Ferrer et al. All rights reserved. Korovkin-Type Theorems for Modular --Statistical Convergence Sat, 31 Jan 2015 13:22:48 +0000 http://www.hindawi.com/journals/jfs/2015/160401/ We deal with a new type of statistical convergence for double sequences, called --statistical convergence, and we prove a Korovkin-type approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to moment-type operators in Orlicz spaces. Carlo Bardaro, Antonio Boccuto, Kamil Demirci, Ilaria Mantellini, and Sevda Orhan Copyright © 2015 Carlo Bardaro et al. All rights reserved. Tricorns and Multicorns of -Iteration Scheme Wed, 28 Jan 2015 12:03:57 +0000 http://www.hindawi.com/journals/jfs/2015/417167/ Complex graphics of dynamical system have striking features of fractals and become a wide area of research due to their beauty and complexity of their nature. The aim of this paper is to study dynamics of relative superior tricorns and multicorns using -iteration schemes. Several examples are presented to explore the geometry of relative superior tricorns and multicorns for antipolynomial of complex polynomial for . Shin Min Kang, Arif Rafiq, Abdul Latif, Abdul Aziz Shahid, and Young Chel Kwun Copyright © 2015 Shin Min Kang et al. All rights reserved. Nontrivial Solutions for Periodic Schrödinger Equations with Sign-Changing Nonlinearities Thu, 15 Jan 2015 14:02:06 +0000 http://www.hindawi.com/journals/jfs/2015/757153/ We prove a new infinite-dimensional linking theorem. Using this theorem, we obtain nontrivial solutions for strongly indefinite periodic Schrödinger equations with sign-changing nonlinearities. Shaowei Chen, Lishan Lin, and Liqin Xiao Copyright © 2015 Shaowei Chen et al. All rights reserved. Boundedness of Marcinkiewicz Integrals and Their Commutators on Generalized Weighted Morrey Spaces Thu, 15 Jan 2015 11:05:31 +0000 http://www.hindawi.com/journals/jfs/2015/450145/ We will study the boundedness of Marcinkiewicz integrals with rough kernel on the generalized weighted Morrey spaces. We will also prove that the commutator operators formed by a function and Marcinkiewicz integrals are also bounded on the generalized weighted Morrey spaces. Runqing Cui and Zhang Li Copyright © 2015 Runqing Cui and Zhang Li. All rights reserved. Uniform Extendibility of the Bergman Kernel for Generalized Minimal Balls Wed, 14 Jan 2015 14:04:06 +0000 http://www.hindawi.com/journals/jfs/2015/919465/ We consider a class of convex domains which contains non-Reinhardt domains with nonsmooth boundary. We show that the domains of this class satisfy the condition Q. Jong-Do Park Copyright © 2015 Jong-Do Park. All rights reserved. Caristi Type Selections of Multivalued Mappings Sun, 11 Jan 2015 07:18:07 +0000 http://www.hindawi.com/journals/jfs/2015/941856/ Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems. Calogero Vetro and Francesca Vetro Copyright © 2015 Calogero Vetro and Francesca Vetro. All rights reserved. Weak Precompactness in the Space of Vector-Valued Measures of Bounded Variation Tue, 06 Jan 2015 08:06:58 +0000 http://www.hindawi.com/journals/jfs/2015/213679/ For a Banach space and a measure space , let be the space of all -valued countably additive measures on of bounded variation, with the total variation norm. In this paper we give a characterization of weakly precompact subsets of . Ioana Ghenciu Copyright © 2015 Ioana Ghenciu. All rights reserved. Two-Weight Extrapolation on Lorentz Spaces Thu, 01 Jan 2015 09:33:34 +0000 http://www.hindawi.com/journals/jfs/2015/182921/ We give several two-weight extrapolation theorems on Lorentz spaces which extend the results of Cruz-Uribe and Pérez (2000) and some applications for the singular integral operators, the potential type operators, and commutators. Wenming Li, Tingting Zhang, and Limei Xue Copyright © 2015 Wenming Li et al. All rights reserved. A Note on the Generalized Camassa-Holm Equation Thu, 25 Dec 2014 12:59:25 +0000 http://www.hindawi.com/journals/jfs/2014/975925/ We study the generalized Camassa-Holm equation which contains the Camassa-Holm (CH) equation and Novikov equation as special cases with the periodic boundary condition. We get a blow-up scenario and obtain the global existence of strong and weak solutions under suitable assumptions, respectively. Then, we construct the periodic peaked solutions and apply them to prove the ill-posedness in with . Yun Wu and Ping Zhao Copyright © 2014 Yun Wu and Ping Zhao. All rights reserved. Global Existence and Blow-Up for the Euler-Bernoulli Plate Equation with Variable Coefficients Thu, 25 Dec 2014 00:10:16 +0000 http://www.hindawi.com/journals/jfs/2014/176429/ We prove the local existence, blow-up, global existence, and stability of solutions to the initial boundary value problem for Euler-Bernoulli plate equation with variable coefficients. Jianghao Hao and Jie Lan Copyright © 2014 Jianghao Hao and Jie Lan. All rights reserved. Some Topological Properties of Mon, 22 Dec 2014 00:10:16 +0000 http://www.hindawi.com/journals/jfs/2014/195262/ If is a completely regular space, first we characterize those spaces whose compact sets are metrizable. Then we use this result to provide a general condition for to ensure the metrizability of compact sets in . Finally, we characterize those spaces that have a -basis. Juan Carlos Ferrando Copyright © 2014 Juan Carlos Ferrando. All rights reserved. Lipschitz Estimates for One-Sided Cohen’s Commutators on Weighted One-Sided Triebel-Lizorkin Spaces Mon, 08 Dec 2014 12:22:45 +0000 http://www.hindawi.com/journals/jfs/2014/720875/ We introduce one-sided Cohen’s commutators of singular integral operators and fractional integral operators, respectively. Using the extrapolation of one-sided weights, we establish the boundedness of these operators from weighted Lebesgue spaces to weighted one-sided Triebel-Lizorkin spaces. Xiao Jin Zhang and Xian Ming Hou Copyright © 2014 Xiao Jin Zhang and Xian Ming Hou. All rights reserved.